A new fractional derivative operator with generalized cardinal sine kernel: Numerical simulation

In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann-Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

In this paper, a new fractional derivative operator using the generalized cardinal sine function as a non-singular analytic kernel is proposed. The corresponding fractional integral operator is also provided. The new fractional operators are expressed as sums in terms of the Riemann-Liouville fractional integral operator. An efficient extension of the new fractional operator, including an integrable singular kernel, is introduced to overcome the initialization problem in related differential equations. A numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives is proposed. The proposed fractional operators, developed relations, and numerical method are expected to contribute to the field of fractional calculus.